To provide an understanding of the relationship between the modified thermal concentration galvanic cells (TCG cell) of this invention and prior art cells, the basic concepts associated with galvanic cells are discussed below.
The first concept to consider is that of a metal electrode. A metal electrode is formed when a metal is immersed in a solution of one of its salts. It is referred to as a single electrode and the following reversible reaction occurs,M0⇄M+n+ne  (1)
This is an oxidation reaction. M0 refers to the metal forming an electrode, M+n is the ion of the metal with a positive valence of n, the number of electrons released, and e represents an electron which has a unit negative charge of electricity.
The second concept to consider is that of the reaction rate of a chemical reaction,aA+bB⇄gG+hH  (2)in which a moles of substance A reacts with b moles of B to yield g moles of G and h moles of H. The change in free energy for the reactions has been shown to be, ΔF=−RTIn K+RT In Q  (3)where ΔF is the change in free energy; K represents the equilibrium constant involving the effective concentrations in a state of equilibrium; and Q represents the ratio of the activities of the products to the activities of the reactants, at any specified activities.
The equilibrium constant K, in Equation (3) is defined asK=[(aG)g(aH)h]/[(aA)a(aB)b]  (4)where a represents the effective concentrations in a state of equilibrium. Q of equation (3) represents the ratio of the activities of the product to the activities of the reactants, at any specified activities, as noted before.Q⇄[(aG)g(aH)h]/[(aA)a(aB)b]  (5)
A galvanic cell is formed when two dissimilar single electrodes are immersed in an electrolyte and connected to each other by means of a conductive wire, which constitutes the external electrical circuit of the galvanic cell. Electrons are released at one electrode according to Equation (1). Oxidation, or the loss of electrons, occurs at the anode. The electrons travel through the external circuit to the second electrode, called a cathode. At the cathode the positively charged metallic ions in, the electrolyte, called cations, undergo a reduction reaction in which the positively charged cation receives electrons to form a metal with no electric charge. Thus, the metallic cation becomes an electrically neutral metal atom. The electrical circuit is completed by the migration of negatively charged anions towards the anode to associate with the positively charged metallic cations released at the anode. This internal flow of electrons carried by the anions constitutes the internal circuit of the galvanic cell.
When a galvanic cell operates reversibly at constant temperature and pressure the maximum electrical work produced is related to the change in free energy, ΔF, byΔF=−n F E  (6)in which n refers to the number of moles of electrons transferred, F is the Faraday constant (96,500 coulombs per mole) and E is the voltage developed by the cell, (one volt equals one Joule per coulomb).
Setting equations (3) and (6) equal to each other and solving for E results in E=(RT/nF)In K−(RT/nF)In Q.  (7)
In the preceding equations R is the universal gas constant (8.314 Joules/(degree-mole), T is the absolute thermodynamic temperature, (degrees Kelvin), F is the Faraday Constant (ca. 96,500 coulombs/mole), and n is the number electrons involved in the reaction. When the activities and the products and the reactants of Equation (5) are unity, In Q equals zero, and Equation (2) becomesE0=(RT/nF)(In K)  (9)In this case E is defined as E0 and substituting (6) in (7)E=E0−(RT/nF)(In Q)  (10)
This equation shows the relationship between E, E0, Q and T. E0 is available in tables of oxidation/reduction potential.
The relationships (1) through (10) indicate that the electrical power developed by a galvanic cell can be changed, after the metals for the electrodes has been specified, by changing the metallic salt used, its concentration in the electrolyte, and the temperature of the cell.
The variety of electrodes (p.432, Outlines of Physical Chemistry, Getman and Daniels, 7th Edit. John Wiley and Sons, Inc. New York, 1947.) include:(1) Metal, metal ion, (2) Inert electrode, non-metal in solution non-metal ion, (3) Inert electrode, ions of different valence, (4) Inert electrode, gas ion, (5) Inert electrode, neutral solutes in different states of oxidation, (6) Amalgam electrode ion, (7) Electrode of an insoluble salt ion. Other variables affecting the performance of galvanic cells are associated (1) with the length of path traveled by the ions in solution, (2) the conductance of the electrolyte as a function of temperature and concentration, and (3) the interfacial surface area of the electrode contacting the electrolyte. Since the chemical reactions at the electrodes are essentially heterogeneous in nature, i.e., they occur at the interface between the electrolyte and the metal surface, the surface area of the electrodes becomes important. The number of metal ions formed is directly proportional to the area of the surface contacting the electrolyte.
Ohm's law describes the basic relationships between the factors that govern the transport of electricity through a conductor. It states that the electric current, A (amperes) equals the applied electromotive force V, (volts) divided by the resistance, R (ohms) of the conductor,A=E/R  (11)
The resistance, R (ohms), is defined by the relationshipR=ρI/a  (12)where, ρ is the resistivity of the medium (ohms-length), I is the length of the path through which electrons flow, and a is the cross-sectional area of the medium associated with the flow of the electrons.
This relationship, although developed for homogeneous materials of uniform cross-section, provides for some insight into the design of galvanic cells. The distance separating the electrodes corresponds to I, the length of path; a refers to the smallest cross-sectional area associated with the ionic path between the electrodes, and ρ is the resistivity. The inverse of the resistivity, k=1/ρ, is called the conductivity. Then a combination of Equations (11) and (12) can be written,A=kV(a/I).  (13)
In words, the current (A) developed by a galvanic cell is directly proportional to the conductivity (k) of the electrolyte, the voltage (V) developed and the cross-sectional area (a) of the path between the anode(s) and the cathode(s), and inversely proportional to the length of the path (I) separating them. This implies that the size, shape, and distance between the electrodes as well as the conductivity of the metal composing the electrodes and the conductivity of the electrolyte affects the current developed.
The interaction between the metal electrode and the metal ions in solution occurs at the interface of a solid and a liquid; consequently, it can be considered as heterogeneous. The number of electrons released in the reaction Equation (1) is proportional to the surface area (a′) of the metal at the interface. Consequently, the amperes (A) is some function of a′, and Equation (13) can be written asA′=k′V′(a′/I′).  (14)Where the primed quantities refer to those factors associated with any of the interfaces, liquid/liquid, solid/liquid, or solid/solid boundaries internal or external to the galvanic device. Other additional factors affecting the performance of a cell are the presence or absence of Thomson, Peltier and Seebeck Effects.
Kirchoff's Rules regarding branch points and loops in an electrical circuit are applicable to the series and parallel arrangements of thermo-concentration-galvanic cells. There are four terminals in a thermal concentration galvanic cell so that the number of combinations taken two at a time is equal to six. That means that six possible voltages can be measured at the terminals of the cell. They can vary from zero to a value allowed by the design specifications of the cell.
Because of the complexity of the mechanisms involved in the evaluation of galvanic cells, a practical and heuristic approach is used to evaluate the performance of the thermo-concentration-galvanic cells disclosed here. This approach involves the application of two relationships: the Nernst Equation, and the Arrhenius Equation. One form of the Nernst Equation isE=−(RT/nF)In(a).  (15)
Here, E is the voltage developed by a modified thermocell in which an inert electrode made from an electrically conductive material that does not take place in any oxidation-reduction reaction is substituted for one of the metal electrodes. Its function is to be a source or sink for electrons flowing through the thermocell, thus accommodating the need for the ions in the electrolyte to be oxidized or reduced. The other symbols are described in preceding comments.
Equation (15) is concerned only with the oxidation reaction of the kind described by equation (1). The voltage, measured by a digital voltammeter, is quantified relative to the inert, non-reactive carbon electrode. The current flowing through the cell is measured, and, the internal resistance of the cell can be calculated by using Ohm's Law.
The Arrhenius Equation provides a means to evaluate the effect of temperature on reaction rates,k=A′e−(ΔH/RT)  (16)in which k is a reaction rate, A′ is called a frequency factor, e is the base of the natural logarithm, ΔH is called the heat of activation for the reaction, R is universal gas constant in appropriate form, and T is the absolute thermodynamic temperature in degrees Kelvin. In logarithmic form, (16) becomesIn(k)=In(A′)−(ΔH/RT)  (17)
When the reaction rate k is referred to Equation (1), it can be used as a proxy for the production of electrons at an anode, and hence is the equivalent of A, the amperage developed by the half-cells, or the TCG Cell. Substituting A for k in (16) one measure of the performance of the cell will yield a straight line on a plot of In(A) vs. (1/T).
The Arrhenius Relationship and the Nernst Equation are derived from thermodynamic principles and are applicable to equilibrium reaction rates. Since, in all cases investigated to date, the reactions are spontaneous, the entropy of the system increases. Because of the formation of coordinated complexes of water molecules with the ions in the electrolyte the coordinated complexes move through the electrolyte toward their designated electrodes at a slower speed than the ion itself under the same conditions. As the temperature of the cell is increased, those coordinated complexes break down. Then ionic mobility is increased and the electric current developed by the cell increases.
When the voltage and the amperage of a cell are measured without any load or external resistance, they are called the open circuit voltage, and the open circuit current of the cell. The power of the cell is the product of the voltage and the current, or, V×A. When the cell is connected to an external resistance, or load, the theoretical, maximum power developed by the cell occurs when the internal resistance of the cell is equal to the external resistance of the load.
A classification of galvanic devices that change chemical energy into electrical energy consists of: (1) non-reversible cells, (2) reversible cells, (3) concentration cells, which occur in two forms, and, (4) thermocells.
A non-reversible cell is composed of two dissimilar electrodes, (one may be inert), immersed in an electrolyte composed of a salt of one of the metals dissolved in a solvent. The voltage developed depends on the relative oxidation-reduction potentials of the electrode metals used and many other factors. An oxidation reaction leading to a loss of electrons occurs at one electrode, called the anode. A reduction reaction involving the gain of electrons occurs at the other electrode, called the cathode. The net result is that electrode materials are used up by ion migration from one electrode to the other, or changed by chemical reactions, limiting the life of the cell.
A reversible cell is sometimes called a storage cell, or battery, because it is re-charged when a voltage is imposed on the cell to reverse the chemical changes that occurred during the discharge of the cell.
A concentration cell occurs in two forms. The first kind is called a concentration cell with transference. It is composed of two identical metallic electrodes immersed in electrolytes of differing concentrations composed of a soluble salt of the metal composing the electrodes. The half-cells of the concentration cell are separated from each other by two different means. If a liquid junction is used to connect the two half cells, the cell is called a concentration cell with transference because ions can migrate from one half-cell to the other. If the half-cells do not contain a liquid bridge, and instead are separated by a salt bridge; then no ion migration is allowed between half-cells and the cell is referred to as a ‘concentration cell without transference’.
Cells without a liquid junction can be constructed using different metallic or gaseous electrodes, and, different concentrations of metal (as in an amalgam), or by incorporating different surface areas of the metal in contact with the electrolyte.
Thermocells have three essential parts: (1) two identical single electrodes, (2) immersed in an electrolyte composed of a soluble salt made of the same metal as the electrodes, (3) housed in either the same container, or separate containers that are connected by a conduit filled with the electrolyte. When the electrodes are held at different temperatures, an electromotive force is developed. A modified thermocell is made by replacing one of the metal electrodes with an inert electrodes, for example a carbon electrode. Modified thermocells can be connected in series or in parallel by metal conductors. The resulting thermo-concentration-galvanic is a combination of two or more modified thermocells forming a concentration cell without transference between the half-cells.